[math-fun] A trillion triangles and congruent numbers
<http://www.eurekalert.org/pub_releases/2009-09/aiom-att091809.php> Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. ... The problem, which was first posed more than a thousand years ago, concerns the areas of right-angled triangles. The surprisingly difficult problem is to determine which whole numbers can be the area of a right- angled triangle whose sides are whole numbers or fractions. ... /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
<http://www.eurekalert.org/pub_releases/2009-09/aiom-att091809.php>
Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. ...
The problem, which was first posed more than a thousand years ago, concerns the areas of right-angled triangles. The surprisingly difficult problem is to determine which whole numbers can be the area of a right- angled triangle whose sides are whole numbers or fractions. ...
/Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
That article doesn't motivate the gigantic integers. It should have given Zagier's 157 exemplar: If a:=6803298487826435051217540/411340519227716149383203, b:=411340519227716149383203/21666555693714761309610, c:=224403517704336969924557513090674863160948472041 /8912332268928859588025535178967163570016480830 then a^2+b^2 = c^2, and ab/2 = 157 . It would be nice to know the (logarithms of the) grossest one they found. Also not crystal clear: Does the validity of the computation hinge on Birch&Swinnerton-Dyer? Would finding a conger not in their list refute B&S-D? --rwg
German Shorthair Pointer, Paris-Harrington theorem http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer This is one of the longest well-mixed transposals in Wikipedia. --Ed Pegg Jr
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here? cheers, jj
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either. On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
In Logology, an anagram is used to describe a word or phrase that can be clued by an arrangement of it's letters. Metamorphosis = Promises a moth. Military weapon = Employ it in a war. The Disney Corporation = Deep in cartoon history The Leaning Tower of Pisa = I spot one giant flaw here... What is the square root of nine? = THREE, for an equation shows it! A Transposal is usually reserved for documentable words or phrases that have exactly the same letters. They do not need to share meaning. For example, the longest transposal in Random House 2nd Unabridged is secondary qualities, quasi-considerately Other long transposals from an online dictionary are --- antiparticles paternalistic conservatoire overreactions aristotelian retaliations obscurantist subtractions definability identifiably arthroscopes crapshooters Ed Pegg Jr --- On Wed, 10/7/09, Allan Wechsler <acwacw@gmail.com> wrote: From: Allan Wechsler <acwacw@gmail.com> Subject: Re: [math-fun] German Shorthair Pointer, Paris-Harrington theorem To: "math-fun" <math-fun@mailman.xmission.com> Cc: ed@mathpuzzle.com Date: Wednesday, October 7, 2009, 4:55 PM I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either. On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
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Yeah, but there's an extra e in German Shorthaired-Pointer, so it's not simply transposing the letters. Why are you allowed the extra letter? On Wed, Oct 7, 2009 at 3:10 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
In Logology, an anagram is used to describe a word or phrase that can be clued by an arrangement of it's letters.
Metamorphosis = Promises a moth. Military weapon = Employ it in a war. The Disney Corporation = Deep in cartoon history The Leaning Tower of Pisa = I spot one giant flaw here... What is the square root of nine? = THREE, for an equation shows it!
A Transposal is usually reserved for documentable words or phrases that have exactly the same letters. They do not need to share meaning. For example, the longest transposal in Random House 2nd Unabridged is
secondary qualities, quasi-considerately
Other long transposals from an online dictionary are ---
antiparticles paternalistic conservatoire overreactions aristotelian retaliations obscurantist subtractions definability identifiably arthroscopes crapshooters
Ed Pegg Jr
--- On Wed, 10/7/09, Allan Wechsler <acwacw@gmail.com> wrote:
From: Allan Wechsler <acwacw@gmail.com> Subject: Re: [math-fun] German Shorthair Pointer, Paris-Harrington theorem To: "math-fun" <math-fun@mailman.xmission.com> Cc: ed@mathpuzzle.com Date: Wednesday, October 7, 2009, 4:55 PM
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either.
On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
Note that in the original post, the phrases were "german shorthair pointer" and "paris-harrington theorem". Note that the latter doesn't have a 'd', so we aren't dealing with anagrams or transpositions if we use 'shorthaired'. The 'ed' was introduced in the third post to this thread. On Wed, Oct 7, 2009 at 3:14 PM, Mike Stay <metaweta@gmail.com> wrote:
Yeah, but there's an extra e in German Shorthaired-Pointer, so it's not simply transposing the letters. Why are you allowed the extra letter?
On Wed, Oct 7, 2009 at 3:10 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
In Logology, an anagram is used to describe a word or phrase that can be clued by an arrangement of it's letters.
Metamorphosis = Promises a moth. Military weapon = Employ it in a war. The Disney Corporation = Deep in cartoon history The Leaning Tower of Pisa = I spot one giant flaw here... What is the square root of nine? = THREE, for an equation shows it!
A Transposal is usually reserved for documentable words or phrases that have exactly the same letters. They do not need to share meaning. For example, the longest transposal in Random House 2nd Unabridged is
secondary qualities, quasi-considerately
Other long transposals from an online dictionary are ---
antiparticles paternalistic conservatoire overreactions aristotelian retaliations obscurantist subtractions definability identifiably arthroscopes crapshooters
Ed Pegg Jr
--- On Wed, 10/7/09, Allan Wechsler <acwacw@gmail.com> wrote:
From: Allan Wechsler <acwacw@gmail.com> Subject: Re: [math-fun] German Shorthair Pointer, Paris-Harrington theorem To: "math-fun" <math-fun@mailman.xmission.com> Cc: ed@mathpuzzle.com Date: Wednesday, October 7, 2009, 4:55 PM
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either.
On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike <http://math.ucr.edu/%7Emike> http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Oops! I didn't see that the original post used both shorthair and shorthaired. In any case, though, 'shorthair' is the preferred word for our purposes... On Wed, Oct 7, 2009 at 3:48 PM, Dave Blackston <hyperdex@gmail.com> wrote:
Note that in the original post, the phrases were "german shorthair pointer" and "paris-harrington theorem". Note that the latter doesn't have a 'd', so we aren't dealing with anagrams or transpositions if we use 'shorthaired'. The 'ed' was introduced in the third post to this thread.
On Wed, Oct 7, 2009 at 3:14 PM, Mike Stay <metaweta@gmail.com> wrote:
Yeah, but there's an extra e in German Shorthaired-Pointer, so it's not simply transposing the letters. Why are you allowed the extra letter?
On Wed, Oct 7, 2009 at 3:10 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
In Logology, an anagram is used to describe a word or phrase that can be clued by an arrangement of it's letters.
Metamorphosis = Promises a moth. Military weapon = Employ it in a war. The Disney Corporation = Deep in cartoon history The Leaning Tower of Pisa = I spot one giant flaw here... What is the square root of nine? = THREE, for an equation shows it!
A Transposal is usually reserved for documentable words or phrases that have exactly the same letters. They do not need to share meaning. For example, the longest transposal in Random House 2nd Unabridged is
secondary qualities, quasi-considerately
Other long transposals from an online dictionary are ---
antiparticles paternalistic conservatoire overreactions aristotelian retaliations obscurantist subtractions definability identifiably arthroscopes crapshooters
Ed Pegg Jr
--- On Wed, 10/7/09, Allan Wechsler <acwacw@gmail.com> wrote:
From: Allan Wechsler <acwacw@gmail.com> Subject: Re: [math-fun] German Shorthair Pointer, Paris-Harrington theorem To: "math-fun" <math-fun@mailman.xmission.com> Cc: ed@mathpuzzle.com Date: Wednesday, October 7, 2009, 4:55 PM
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either.
On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike <http://math.ucr.edu/%7Emike> http://reperiendi.wordpress.com
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I think what caused the trouble is that German_Shorthair_Pointer redirects to German_Shorthaired_Pointer on Wikipedia... On Wed, Oct 7, 2009 at 3:49 PM, Dave Blackston <hyperdex@gmail.com> wrote:
Oops! I didn't see that the original post used both shorthair and shorthaired. In any case, though, 'shorthair' is the preferred word for our purposes...
On Wed, Oct 7, 2009 at 3:48 PM, Dave Blackston <hyperdex@gmail.com> wrote:
Note that in the original post, the phrases were "german shorthair pointer" and "paris-harrington theorem". Note that the latter doesn't have a 'd', so we aren't dealing with anagrams or transpositions if we use 'shorthaired'. The 'ed' was introduced in the third post to this thread.
On Wed, Oct 7, 2009 at 3:14 PM, Mike Stay <metaweta@gmail.com> wrote:
Yeah, but there's an extra e in German Shorthaired-Pointer, so it's not simply transposing the letters. Why are you allowed the extra letter?
On Wed, Oct 7, 2009 at 3:10 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
In Logology, an anagram is used to describe a word or phrase that can be clued by an arrangement of it's letters.
Metamorphosis = Promises a moth. Military weapon = Employ it in a war. The Disney Corporation = Deep in cartoon history The Leaning Tower of Pisa = I spot one giant flaw here... What is the square root of nine? = THREE, for an equation shows it!
A Transposal is usually reserved for documentable words or phrases that have exactly the same letters. They do not need to share meaning. For example, the longest transposal in Random House 2nd Unabridged is
secondary qualities, quasi-considerately
Other long transposals from an online dictionary are ---
antiparticles paternalistic conservatoire overreactions aristotelian retaliations obscurantist subtractions definability identifiably arthroscopes crapshooters
Ed Pegg Jr
--- On Wed, 10/7/09, Allan Wechsler <acwacw@gmail.com> wrote:
From: Allan Wechsler <acwacw@gmail.com> Subject: Re: [math-fun] German Shorthair Pointer, Paris-Harrington theorem To: "math-fun" <math-fun@mailman.xmission.com> Cc: ed@mathpuzzle.com Date: Wednesday, October 7, 2009, 4:55 PM
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either.
On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike <http://math.ucr.edu/%7Emike> http://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
I think that if you take the ED off SHORTHAIR-ED, then the anagram is exact. R. On Wed, 7 Oct 2009, Allan Wechsler wrote:
I don't think there is one, JJ. I think the point is that PARIS HARRINGTON THEOREM and GERMAN SHORTHAIRED POINTER are something like anagrams. Something like, but not exactly, so I'm not sure what Ed means either.
On Wed, Oct 7, 2009 at 2:53 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Oct 07. 2009 17:46]:
German Shorthair Pointer, Paris-Harrington theorem
http://en.wikipedia.org/wiki/Paris-Harrington_theorem http://en.wikipedia.org/wiki/German_Shorthaired_Pointer
This is one of the longest well-mixed transposals in Wikipedia.
--Ed Pegg Jr
What is the connection to congruent numbers here?
cheers, jj
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participants (8)
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Allan Wechsler -
Bernie Cosell -
Dave Blackston -
Ed Pegg Jr -
Joerg Arndt -
Mike Stay -
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